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   <h4 class="subsectionHead"><span class="titlemark">2.5   </span> <a 
 id="x10-210002.5"></a>Plane Strain Elements</h4>
<!--l. 613--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.5.1   </span> <a 
 id="x10-220002.5.1"></a>Quad1PlaneStrain</h5>
<!--l. 614--><p class="noindent" >Represents isoparametric four-node quadrilateral plane-strain finite element. Each node has 2 degrees of freedom.
Structure should be defined in x,y plane. The nodes should be numbered anti-clockwise (positive rotation around
z-axis). The element features are summarized in Table&#x00A0;<a 
href="#x10-2200216">16<!--tex4ht:ref: quad1planestrainsummary --></a>.
<!--l. 620--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x10-220019"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure8.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;9: </span><span  
class="content">Quad1PlaneStrain element. Node numbering, Side numbering and definition of local edge c.s.(a).</span></div><!--tex4ht:label?: x10-220019 -->
                                                                                           
                                                                                           
<!--l. 628--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 630--><p class="noindent" >
<div class="table">
<!--l. 630--><p class="noindent" ><a 
 id="x10-2200216"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-17" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-17-1g"><col 
id="TBL-17-1"></colgroup><colgroup id="TBL-17-2g"><col 
id="TBL-17-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-17-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-17-1-2"  
class="td11"><!--l. 630--><p class="noindent" ><span 
class="cmbx-10">quad1planestrain</span>                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-2-2"  
class="td11"><!--l. 630--><p class="noindent" >2D linear quadrilateral plane-strain element                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-17-3-2"  
class="td11"><!--l. 630--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-17-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-4-2"  
class="td11"><!--l. 631--><p class="noindent" ><span 
class="cmtt-10">NIP</span>:  allows  to  set  the  number  of  integration  points  for
integration of membrane terms.                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-5-2"  
class="td11"><!--l. 632--><p class="noindent" >Two dofs (u-displacement, v-displacement) are required in
each node.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-6-2"  
class="td11"><!--l. 633--><p class="noindent" >Linear approximation of displacements and geometry.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-7-2"  
class="td11"><!--l. 636--><p class="noindent" >Integration   of   membrane   strain   terms   using   gauss
integration formula in 4 (the default), 9 or 16 integration
points. The default number of integration points used can
be overloaded using <span 
class="cmtt-10">NIP </span>parameter. Reduced integration for
shear terms is employed. Shear terms are always integrated
using 1 point integration rule.                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-8-2"  
class="td11"><!--l. 637--><p class="noindent" >Nonlocal constitutive support, Adaptivity support.          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-9-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-9-2"  
class="td11"><!--l. 638--><p class="noindent" >Cross section thickness is required.                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-10-2"  
class="td11"><!--l. 641--><p class="noindent" >Body loads are supported. Boundary loads are supported
and  computed  using  numerical  integration.  The  side
numbering  is  following.  Each  i-th  element  side  begins
in  i-th  element  node  and  ends  on  next  element  node
(i+1-th  node  or  1-st  node,  in  the  case  of  side  number
4).  The  local  positive  edge  x-axis  coincides  with  side
direction, the positive local edge y-axis is rotated 90 degrees
anti-clockwise (see fig. (<a 
href="#x10-220019">9<!--tex4ht:ref: Quad1PlaneStrainfig --></a>)).                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-11-1"  
class="td11">Nlgeo                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-11-2"  
class="td11"><!--l. 642--><p class="noindent" >0.                                                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-17-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-17-12-2"  
class="td11"><!--l. 643--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-17-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-17-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-17-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;16: </span><span  
class="content">quad1planestrain element summary</span></div><!--tex4ht:label?: x10-2200216 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.5.2   </span> <a 
 id="x10-230002.5.2"></a>TrplaneStrain</h5>
<!--l. 651--><p class="noindent" >Implements an triangular three-node constant strain plane-strain finite element. Each node has 2 degrees of freedom.
The node numbering is anti-clockwise. The element features are summarized in Table&#x00A0;<a 
href="#x10-2300217">17<!--tex4ht:ref: trplanestrainsummary --></a>.
<!--l. 655--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x10-2300110"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure9.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;10: </span><span  
class="content">TrplaneStrain element - node and side numbering.</span></div><!--tex4ht:label?: x10-2300110 -->
                                                                                           
                                                                                           
<!--l. 662--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 664--><p class="noindent" >
<div class="table">
<!--l. 664--><p class="noindent" ><a 
 id="x10-2300217"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-18" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-18-1g"><col 
id="TBL-18-1"></colgroup><colgroup id="TBL-18-2g"><col 
id="TBL-18-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-18-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-18-1-2"  
class="td11"><!--l. 664--><p class="noindent" ><span 
class="cmbx-10">trplanestrain</span>                                                  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-2-2"  
class="td11"><!--l. 664--><p class="noindent" >2D linear triangular plane-strain element                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-18-3-2"  
class="td11"><!--l. 664--><p class="noindent" >-                                                                            </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-18-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-4-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-4-2"  
class="td11"><!--l. 666--><p class="noindent" >Two dofs (u-displacement, v-displacement) are required in
each node.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-5-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-5-2"  
class="td11"><!--l. 667--><p class="noindent" >Linear approximation of displacements and geometry.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-6-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-6-2"  
class="td11"><!--l. 668--><p class="noindent" >Integration of membrane strain terms using one point gauss
integration formula.                                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-7-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-7-2"  
class="td11"><!--l. 669--><p class="noindent" >Nonlocal   constitutive   support.   Edge   load   support,
Adaptivity support.                                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-8-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-8-2"  
class="td11"><!--l. 670--><p class="noindent" >Cross section thickness is required.                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-9-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-9-2"  
class="td11"><!--l. 673--><p class="noindent" >Body loads are supported. Boundary loads are supported
and are computed using numerical integration. The side
numbering  is  following.  Each  i-th  element  side  begins
in  i-th  element  node  and  ends  on  next  element  node
(i+1-th  node  or  1-st  node,  in  the  case  of  side  number
3).  The  local  positive  edge  x-axis  coincides  with  side
direction, the positive local edge y-axis is rotated 90 degrees
anti-clockwise (see fig. (<a 
href="#x10-2300110">10<!--tex4ht:ref: TrplaneStrain --></a>)).                                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-10-1"  
class="td11">Nlgeo                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-10-2"  
class="td11"><!--l. 674--><p class="noindent" >0.                                                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-18-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-18-11-2"  
class="td11"><!--l. 675--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-18-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-18-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-18-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;17: </span><span  
class="content">trplanestrain element summary</span></div><!--tex4ht:label?: x10-2300217 -->
</div><hr class="endfloat" />
</div>
</div>
                                                                                           
                                                                                           
                                                                                           
                                                                                           
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